French authorities are refusing to comment on how the Berlin attack suspect apparently crossed into France and left again in the face of an international manhunt.

Anis Amri was fatally shot today when he opened fire on police in Milan, Italy, who stopped him for a routine ID check.

Milan's police chief says Amri had ``surely passed through France'' _ a country that has been living in a state of emergency for more than a year after deadly Islamic extremist attacks.

France upped security on the road borders with Germany border after Monday's Christmas market attack in Berlin, and introduced extra security forces on trains last year after American passengers thwarted an attack on an Amsterdam-Paris route.

The Interior Ministry, prime minister's office and president's office would not comment on the Milan police announcement that Amri was found in Italy with a train ticket from Chambery, France the day before.

French Interior Minister Bruno Le Roux visited a Paris train station Friday morning to inspect security measures ahead of Christmas holidays. He said more than 91,000 police and military forces are deployed across the country.

In a related story, a video released by the Islamic State group shows the Tunisian suspect in the Berlin truck attack pledging allegiance to its leader Abu Bakr al-Baghdadi and vowing to fight against what he calls ``the Crusader pigs.''

The video, which appeared to have been taken by Anis Amri himself, shows him standing on a footbridge in the north of Berlin, not far from where he allegedly hijacked the truck used in the attack that killed 12 people and injured dozens more at a Christmas market on Monday.